论文标题
自组织地图与高斯混合模型之间的严格联系
A Rigorous Link Between Self-Organizing Maps and Gaussian Mixture Models
论文作者
论文摘要
这项工作提出了对自组织图（SOMS）和高斯混合模型（GMM）之间关系的数学处理。我们表明，基于能量的SOM模型可以解释为执行梯度下降，最大程度地降低了与GMM对数可能性的近似值，这对于高数据维度特别有效。邻域半径的类似SOM样减小可以理解为一种退火程序，以确保梯度下降不会卡在不良的局部最小值中。该链接允许将SOM视为生成概率模型，从而为使用SOM（例如检测异常值或采样）提供了正式的理由。
This work presents a mathematical treatment of the relation between Self-Organizing Maps (SOMs) and Gaussian Mixture Models (GMMs). We show that energy-based SOM models can be interpreted as performing gradient descent, minimizing an approximation to the GMM log-likelihood that is particularly valid for high data dimensionalities. The SOM-like decrease of the neighborhood radius can be understood as an annealing procedure ensuring that gradient descent does not get stuck in undesirable local minima. This link allows to treat SOMs as generative probabilistic models, giving a formal justification for using SOMs, e.g., to detect outliers, or for sampling.
